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A199950 Decimal expansion of greatest x satisfying x^2 + cos(x) = 2*sin(x).

%I A199950 #13 Feb 08 2025 22:59:53
%S A199950 1,2,7,1,0,2,6,8,0,0,8,1,5,9,4,6,0,6,4,0,0,4,7,1,8,8,4,8,0,9,7,8,5,0,
%T A199950 2,6,8,3,5,6,7,1,1,8,3,7,6,7,9,9,9,2,6,8,7,3,8,7,9,6,8,1,1,5,1,0,2,3,
%U A199950 1,8,6,7,8,7,9,3,0,1,8,4,4,1,3,4,8,9,7,8,1,8,9,6,1,6,3,0,1,2,9
%N A199950 Decimal expansion of greatest x satisfying x^2 + cos(x) = 2*sin(x).
%C A199950 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199950 G. C. Greubel, <a href="/A199950/b199950.txt">Table of n, a(n) for n = 1..10000</a>
%H A199950 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199950 least x:  0.659266045766946074537348579563067611...
%e A199950 greatest x: 1.271026800815946064004718848097850268...
%t A199950 a = 1; b = 1; c = 2;
%t A199950 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199950 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199950 r = x /. FindRoot[f[x] == g[x], {x, .65, .66}, WorkingPrecision -> 110]
%t A199950 RealDigits[r]   (* A199949 *)
%t A199950 r = x /. FindRoot[f[x] == g[x], {x, 1.27, 1.28}, WorkingPrecision -> 110]
%t A199950 RealDigits[r]   (* A199950 *)
%o A199950 (PARI) a=1; b=1; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A199950 Cf. A199949.
%K A199950 nonn,cons
%O A199950 1,2
%A A199950 _Clark Kimberling_, Nov 12 2011